Turkish troops clashed with Kurdish militants in the snowy mountains of northern Iraq on Friday after staging a surprise invasion, the most serious offensive in years in Turkey's long-running fight against anti-government rebels.

Iraq's government reacted angrily, demanding the troops' withdrawal and accusing Turkey of destroying five bridges despite its pledge to target only rebel bases.

The invasion could inflame ethnic tensions in what has been the most peaceful part of Iraq. Iraqi Kurds sympathize with Turkish Kurds' quest for autonomy and want to expand Iraq's own autonomous Kurdistan region. Arabs in northern Iraq, however, fear that greater Kurdish clout will sideline them.

Turkish President Abdullah Gul called President Bush early Thursday to tell him of the impending incursion, according to Turkey's military. Secretary of State Condoleezza Rice urged Turkey to keep the operation short and "keep in mind that while the terrorists need, obviously, to be stopped from doing what they're doing, that there really can't be a destabilization of the region."

White House spokesman Scott Stanzel suggested the United States had shared intelligence with Turkey, a NATO ally, before the incursion.

After hours of bombing and shelling by Turkish artillery and warplanes, Turkish soldiers crossed via the Habur mountain pass after dusk Thursday into a sparsely populated corner of northern Iraq that the Kurdish separatist group, known as the Kurdistan Workers' Party, or PKK, has used as a refuge and a base for attacks on Turkey.

The number of Turkish troops in Iraq remained unclear Friday, but American and Iraqi officials estimated there were 500 to 1,000. Turkish television reported the number was as high as 10,000.

Ahmed Denize, a member of the PKK, said small teams of guerrillas fought Turkish soldiers throughout the day in Iraq. "We had information that they are coming, so we spread out in small groups and opened fire on them," he said. "The fight is still going on."

The semiofficial Anatolia news agency reported that the Turkish military said 24 PKK fighters were killed, along with five Turkish soldiers.

Turkish Prime Minister Recep Tayyip Erdogan said the military "will rapidly return (to Turkey) as soon as it reaches its aim," which he said is the elimination of PKK hideouts.

The Kurdish fighters hiding in Iraq want more rights for the large Kurdish population in Turkey and have, at times, advocated an independent Kurdish state in the region. The smoldering tensions flared in October, when Kurdish rebels killed 12 Turkish soldiers near the border with northern Iraq.

Turkish politicians threatened an invasion and have said they will do what is necessary to protect their people from rebel attacks. Throughout the fall and winter, Turkey bombed PKK positions along the border, but until Thursday night, it had stopped short of crossing into Iraqi territory.

The conflict, which began when PKK rebels took up arms against Turkey's government in 1984, has put the Bush administration in an awkward position as it juggles its alliance with Turkey with its need to keep peace in northern Iraq. Some Iraqi Kurdish political leaders have pressed the United States to intervene militarily, but it has limited its involvement to diplomacy.

Turkey's invasion was the biggest since before 2003, when U.S. forces moved into Iraq. "This has been a serious escalation," Iraqi Foreign Minister Hoshyar Zebari said. "We hope that this will end as soon as possible for fear of escalation or any minor mistakes that would lead to a wider problem."

He said Turkish forces destroyed five bridges, "contrary to the promises made by the Americans or other sides that the Turkish forces won't target the infrastructure or population."